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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 903–912

Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas

Vadim A. Markel, Joseph A. O’Sullivan, and John C. Schotland  »View Author Affiliations


JOSA A, Vol. 20, Issue 5, pp. 903-912 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000903


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Abstract

We continue our study of the inverse scattering problem for diffuse light. In contrast to our earlier work, in which we considered the linear inverse problem, we now consider the nonlinear problem. We obtain a solution to this problem in the form of a functional series expansion. The first term in this expansion is the pseudoinverse of the linearized forward-scattering operator and leads to the linear inversion formulas that we have reported previously. The higher-order terms represent nonlinear corrections to this result. We illustrate our results with computer simulations in model systems.

© 2003 Optical Society of America

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.6960) Medical optics and biotechnology : Tomography

Citation
Vadim A. Markel, Joseph A. O’Sullivan, and John C. Schotland, "Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas," J. Opt. Soc. Am. A 20, 903-912 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-903


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References

  1. V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. I. Fourier–Laplace inversion formulas,” J. Opt. Soc. Am. A 18, 1336–1347 (2001).
  2. V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. II. Inversion with boundary conditions,” J. Opt. Soc. Am. A 19, 558–566 (2002).
  3. V. A. Markel and J. C. Schotland, “Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition,” J. Opt. Soc. Am. A 20, 890–902 (2002).
  4. R. Aronson, “Boundary conditions for diffuse light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
  5. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
  6. H. E. Moses, “Calculation of the scattering potential from reflection coefficients,” Phys. Rev. 102, 550–567 (1956).
  7. R. T. Prosser, “Formal solutions of the inverse scattering problem,” J. Math. Phys. 10, 1819–1822 (1969).
  8. R. Snieder, “A perturbative analysis of non-linear inversion,” Geophys. J. Int. 101, 545–556 (1990).
  9. G. A. Tsihrintzis and A. J. Devaney, “A Volterra series approach to nonlinear travel time tomography,” IEEE Trans. Geosci. Remote Sens. 38, 1733–1742 (2000).
  10. V. A. Markel and J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E 64, R035601 (2001).
  11. P. S. Carney and J. C. Schotland, “Inverse scattering for near-field microscopy,” Appl. Phys. Lett. 77, 2798–2800 (2000).
  12. P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev. Lett. 86, 5874–5877 (2001).
  13. P. S. Carney and J. C. Schotland, “Three-dimensional total internal reflection microscopy,” Opt. Lett. 26, 1072–1074 (2001).
  14. P. S. Carney and J. C. Schotland, “Determination of three-dimensional structure in photon scanning tunneling microscopy,” J. Opt. A 4, S140–S144 (2002).
  15. V. A. Markel and J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
  16. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 19, 4887–4891 (1994).

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